NGC 7314: X-ray Study of the Evolving Accretion Properties

We used a total of 92 archival data of the proportional counter array (PCA) onboard RXTE (Bradt et al., 1993) from January 01, 1999 (MJD=51179.74) to July 16, 2000 (MJD=51741.09) and from July 19, 2002 (MJD=52474.22) to July 22, 2002 (MJD=52477.71). We followed the standard procedure to extract the PCU2 spectra described in ’The ABC of XTE’³³3https://heasarc.gsfc.nasa.gov/docs/xte/abc/front_page.html. For the spectral analysis, we use Standard2f mode data with 16-s time resolution, which has 128 energy channels. Spectra are extracted only from PCU2. We generated a background fits file using the PCABACKEST tool and the ’bright’ background model appropriate for our observation periods. A good time interval (GTI) file is created using the FTOOLS task maketime to include only periods when the instrument operates under optimal conditions. The saextrct tool was used to extract the source spectra and background spectra using the GTI file. To improve the signal-to-noise ratio, we rebinned the spectra using the rbnpha tool, combining adjacent energy channels to ensure each bin had a minimum number of counts. The spectra were rebinned to have at least 5 counts/bin to obtain valid $\chi^{2}$ statistics. We then generated the response matrix and effective area files using the pcarsp tool to account for the instrumental response.

NuSTAR observed NGC 7314 on May 13, 2016. NuSTAR consists of two identical focal plane modules- FPMA and FPMB (Harrison et al., 2013). The NuSTAR raw data was reprocessed using the NuSTAR Data Analysis Software (NuSTARDAS version 2.1.2). Calibrated and cleaned event files were generated by nupipeline task. We used 20200912 version of calibration files from NuSTAR calibration database⁴⁴4http://heasarc.gsfc.nasa.gov/FTP/caldb/data/nustar/fpm/. We used 60” circular regions to extract both the source and background spectra. The background region was selected far away from the source region of the same chip. The light curves and spectra were produced from the cleaned science mode event files through nuproducts task. Light curves were extracted with 300 sec time binning. The light curves from two modules were combined with lcmath task. For the variability study, we produced $3-10$ keV (soft band), $10-78$ keV, and $3-78$ keV light curves. We rebinned the $3-78$ keV spectra with 20 counts/bin using grppha task.

NGC 7314 was first observed on May 02, 2001 by XMM-Newton. Among the two observations on that day, we used only ObsId. 0111790101 for its comparatively high exposure. We also used two observations 0725200101 and 0725200301, from May 17, 2013, and November 28, 2013. For a simultaneous study with the NuSTAR observation, we used ObsId. 0790650101 from May 14, 2016 with 65 ks exposure. The observation data files (ODFs) from the European Photon Imaging Camera (EPIC) on the detector were processed using the Science Analysis System (SAS; Gabriel et al. 2004) version 20.0.0). We followed standard procedures⁵⁵5https://www.cosmos.esa.int/web/xmm-newton/sas-threads to obtain calibrated and concatenated event lists, by filtering them for periods of high background flaring activity, and by extracting the light curves and spectra. The source events were extracted using a circular region, with a radius of 36” arcsec, centered on the target, and the background events were extracted from a circular region, with a radius of 40” arcsec, on the same chip far from the source. We verified that the photon pile-up is negligible in the filtered event list with the task epatplot. After that, the response matrix files (RMFs) and ancillary response files (ARFs) were generated, and the spectra were re-binned in order to include a minimum of 25 counts in each background-subtracted spectral channel and, also, in order to not oversample the intrinsic energy resolution by a factor larger than 3. We have also extracted $0.2-3$ keV, $3-10$ keV, and $0.2-10$ keV light curves for the four XMM-Newton observations with 300 sec binning to study the variability. We followed the procedure in the webpage⁶⁶6https://www.cosmos.esa.int/web/xmm-newton/sas-thread-timing for extracting light curves.

In X-ray binary studies, it is customary to examine timing properties using Power Spectral Densities (PSDs) averaged over multiple light curves to reduce noise (van der Klis, 1995). However, AGN studies often rely on single light curves due to limited data, which can be misleading, as fluctuations in variance may simply reflect the stochastic nature of the process rather than genuine physical changes Papadakis & Lawrence (1993); Uttley et al. (2002). The excess variance statistic ($F_{\rm var}$) can be employed to quantify variability in AGNs, even with limited observational data. The excess variance can reveal valuable information despite the difficulties of robustly estimating variability amplitudes from short observations. For instance, it has been shown that the variability amplitude in Seyfert 1 galaxies is inversely correlated with the source luminosity (Nandra et al., 1997; Leighly, 1999; Markowitz & Edelson, 2001). Additionally, differences in the normalized excess variance between energy bands can indicate energy-dependent PSDs or independently varying spectral components, further enriching our understanding of AGN variability.

To characterize the extent of variability in our data, we utilized the normalized excess variance ($F_{\rm var}$) as a measure. The $F_{\rm var}$ parameter, introduced by Edelson et al. (2002) and further discussed by Vaughan et al. (2003), enables us to quantify the intrinsic variations of the source while mitigating the impact of measurement errors.

In accordance with the methodology outlined in Vaughan et al. (2003), we define the $F_{\rm var}$ as follows:

In this equation, $S^{2}$ denotes the sample variance, $\bar{x}$ represents the arithmetic mean of the data points $x_{i}$, and $\bar{\sigma}^{2}_{\rm err}$ is the average of the squared measurement errors.

The values of $S^{2}$ and ${\bar{\sigma}^{2}_{\rm err}}$ are computed as follows:

To estimate the uncertainty associated with the $F_{\rm var}$ value, we use the following formula:

This equation takes into account the contribution of both the variance in measurement errors and the uncertainties related to the mean and $F_{\rm var}$ value.

We produced $3-10$ keV, $10-78$ keV, and $3-78$ keV NuSTAR light curves to study the variability. The top, middle, and bottom panels of Figure 1 show the light curve in the (a) $3-10$ keV (soft band), (b) $10-78$ keV (hard band), and (c) $3-78$ keV (total) energy range, respectively. We have calculated the fractional variability ($F_{\rm var}$) of the three energy bands’ light curves to study the variability (Edelson et al., 2002; Vaughan et al., 2003). The $F_{\rm var}$ of these soft, hard, and total bands light curves are found to be $0.270\pm 0.003$, $0.196\pm 0.006$, and $0.249\pm 0.003$, respectively. We have also calculated the variability of the light curves of four XMM-Newton observations (see, Figure 2). All the values of F_var for different energy ranges are given in Table 2. We notice that the soft band (0.2-3 keV for XMM-Newton or 3-10 keV for NuSTAR) variability is always greater than the hard band (3-10 keV for XMM-Newton or 10-78 keV for NuSTAR) variability. Also, a consistent increase in the variability can be seen from 2001 to 2013 XMM-Newton observations, while it decreases after that in the 2016 observation.

We use HeaSoft’s spectral analysis package XSPEC⁷⁷7https://heasarc.gsfc.nasa.gov/xanadu/xspec/(Arnaud, 1996) version 12.12.1 to fit the data. We make use of two Tbabs absorption models throughout our study for the line-of-sight absorption. Two absorption models are used to represent the Galactic and intrinsic line-of-sight absorption. The Galactic absorption was fixed at $1.45\times 10^{20}$ cm^-2(Dickey & Lockman, 1990). We use vern scattering (Verner et al., 1996) and wilm abundances (Wilms et al., 2000). The line of sight column density ($N_{\rm H}$) is kept free during the spectral fitting. $\chi^{2}$ statistic is used to determine the goodness of the fits. We use multiplicative model component constant as cross-normalization between the different spectra. We fixed the constant parameter at the unit value for the first spectrum while letting it vary for other spectra for simultaneous fit. Tbabs and zTbabs are used for the Galactic and intrinsic absorption.

We study the accretion properties of narrow-line Seyfert NGC 7314 using RXTE, XMM-Newton, and NuSTAR data. The timing analysis conducted on NGC 7314 using NuSTAR revealed significant variability across different energy bands ($F_{\rm var}$ $\sim$ $0.270\pm 0.003$ (3-10 keV), $0.196\pm 0.006$ (10-78 keV), and $0.249\pm 0.003$ (3-78 keV)). We also estimate the variability of light curves from XMM-Newton data. For both the case of NuSTAR and XMM-Newton, we see a similar pattern on the light curve in the soft and hard bands. We notice that both in the soft (0.2-3 keV) and hard (3-10 keV) energy bands in the XMM-Newton light curves, the variability increases (0.191$\pm$0.002 to 0.282$\pm$0.002 in soft; 0.184$\pm$0.003 to 0.262$\pm$0.003 in hard) from 2001 to 2013. In 2016, the variability again showed lower values both in the soft ($\sim$0.223$\pm$0.002) and hard energy bands ($\sim$0.219$\pm$0.003). Also, we notice that the variability in the soft energy bands (i.e., 0.2-3 keV for XMM-Newton and 3-10 keV for NuSTAR) is always higher than the variability in the hard energy bands (i.e., 3-10 keV for XMM-Newton and 10-78 keV for NuSTAR), which is more significantly verified in case of the NuSTAR observation. This implies that the high variability mainly comes from the soft X-ray emitting region. The fractional variability ($F_{\rm var}$) values obtained for the soft, hard, and total energy bands were consistent with previous studies and indicated the presence of intrinsic variability in the source. We also notice similar types of variation in both the soft and hard energy bands. These results suggest the existence of dynamic processes within NGC 7314, such as accretion disk instabilities or changes in the coronal emission region. A possible explanation could be that the primary soft X-ray continuum is a variable source, produced in some hot corona closer to the SMBH, while the high energy photons are produced from the scattering of these primary X-ray photons by a constant temperature high energy cloud, located away from the SMBH (see also, Lawrence et al. (1985) for spectral changes in NGC 4051). The variable soft-X rays thus get into multiple scattering and come out as more smooth-amplitude high-energy light curves. Also, the increase and decrease in the values of the $F_{\it var}$ indicates a change in the inner accretion properties that happened during the 2001 to 2013 period, and the reverse phenomenon happened during the 2013 to 2016 period.

We analyze combined XMM-Newton and NuSTAR data for a broadband study of the accretion properties of NGC 7314. In the spectral analysis, we employed various models (a combination of phenomenological and physical) to unravel the emission components and their evolution over time.

The combined spectrum of XMM-Newton and NuSTAR is best fitted with model 4. From the combined spectral fit, we obtain a low inner edge of the accretion disk, a moderate inclination angle, and a relatively high spin value. The spectrum shows a clear signature of an absorption component around $1.35$ keV and a soft excess component with a peak around 0.05 keV. Fe K$\alpha$ lines come from two different regions- one from some high ionization region and one from a low (or neutral) ionization region.

To study the evolution, we study the four XMM-Newton spectra (see, Table4). We obtain spin parameter ($a\sim 0.65^{+0.12}_{-0.13}$) and inclination angle ($\theta\sim 45^{\circ}~{}^{+2.15}_{-1.81}$) from the simultaneous fitting of the XMM observations. The spectral analysis of four XMM-Newton data revealed a change in the accretion properties. These variations could be attributed to changes in the accretion flow, the geometry of the emitting regions, or variations in the intrinsic source properties. In Table 4, although not significant for all, a few parameters show similar values in the 2001 and 2016 observations. These changes indicate a mild state transition from 2001 to 2013 and retracing back again to 2016.

The change in the inner disk radius ($R_{\rm in}$) and absorption component Gabs is noticed during this time. Although the photon index ($\Gamma$) has not shown significant change, a rough pattern can be noticed similar to the other parameters. The 2-10 keV luminosities ($L_{2-10keV}$) also show a similar feature.

The variation of the Fe K$\alpha$ line emission and the absorption feature is also noticed in the four XMM-Newton data (May 2, 2001; May 17, 2013; November 28, 2013, and May 5, 2016). The equivalent width of the broad Fe K$\alpha$ line also shows variation during this period. From 2001 to 2013, the equivalent width increased (from 47 eV to 56/66 eV ), then in 2016, it showed a lesser value ($\sim$36 eV).

The long-term analysis of RXTE/PCA data provides insights into the temporal variations of NGC 7314. The weak positive correlation suggests that the $\Gamma$ also increases slightly as the power-law flux increases. This behavior implies that the spectrum becomes softer with increasing flux. This result aligns with the general trend observed in other AGNs, where a positive correlation between $\Gamma$ and the Eddington ratio ($\lambda$) is often found. Previous studies have shown varying degrees of correlation between $\Gamma$ and the $\lambda$. For example, Shemmer et al. (2006) found a strong positive correlation between $\Gamma$ and $\lambda$ in a sample of AGNs, suggesting that higher accretion rates (higher $\lambda$) are associated with softer spectra (higher $\Gamma$). Brightman et al. (2013) also reported a positive correlation between $\Gamma$ and the $\lambda$ in a sample of AGNs, reinforcing the idea that the accretion rate influences the spectral shape. However, Risaliti et al. (2009) noted that the correlation can vary significantly depending on the sample and the specific characteristics of the AGNs studied, indicating that other factors, such as the black hole spin and the geometry of the accretion disk, can also play a significant role.

Our findings for NGC 7314, although showing a weaker correlation compared to some studies, are still consistent with the general trend observed in AGNs. The weak correlation might be due to intrinsic variability in NGC 7314 or differences in the physical conditions of the accretion flow compared to other AGNs. In summary, the positive correlation between $\Gamma$ and the Eddington ratio ($\lambda$) in NGC 7314 supports the idea that higher accretion rates lead to softer X-ray spectra. This is in line with previous studies, although the strength of the correlation in NGC 7314 appears to be weaker.

The pattern of this spectral evolution indicates that NGC 7314 could be a potential changing-state AGN. Although the variation of the spectral properties is not very significant for NGC 7314, a clear trend can be noticed during $\sim$15 years of observations. Almost similar properties can be noticed in Mrk 110 in 2001 when it completely did not shift to type-2, but in some intermediate Seyfert type, classified it as moderately changing state AGN (Porquet et al., 2024).

An absorption component Gabs is required to fit the spectra. The line energy of this absorption component is centered around $1.35\pm 0.03$ keV with a line width of $0.12\pm 0.01$ keV (see model 4).

We also estimate the dust sublimation radius (inner radius of the dusty torus, $R_{\rm dust}$), following the methods of Nenkova et al. (2008a, b),

where $L_{\rm bol}$ and $T_{\rm sub}$ are the bolometric luminosity and dust sublimation temperature. $T_{\rm sub}$ is generally assumed to be the sublimation temperature of graphite grains, $T\sim 1500~{\rm K}$ (Kishimoto et al., 2007). We consider the bolometric luminosity to be $L_{\rm bol}\sim 20\times L_{2-10~{\rm keV}}$(Vasudevan et al., 2009; Duras et al., 2020). We obtain the average dust sublimation radius from the four observations (see, last row of Table 4 for $L_{2-10}$ luminosity) to be 0.05 pc (or $\sim 2\times 10^{17}$ cm). From a study of XMM-Newton, Suzaku, and ASCA data, a coherent depiction of the system’s geometry within the framework of a unified model is given (Ebrero et al., 2011). The diverse observed properties are explained as neutral gas clouds moving across our line of sight. These clouds could possibly be responsible for the absorption feature around 1.3 keV. These clouds could possibly be located between the BLR and the dusty torus since a small variability can be observed in the absorption parameters during our studied period. However, from the line width of the absorption, it is evident that the absorption occurred in some high ionization regions and might be closer than the BLR.

We also estimate the BLR radius ($R_{\rm BLR}$) from the X-ray luminosity (Kaspi et al., 2005).

where $L_{2-10}$ is the $2-10$ keV X-ray luminosity. We obtain the $R_{\rm BLR}$ from the four observations to be 9.08$\times 10^{15}$ cm, 6.90$\times 10^{15}$ cm, 6.24$\times 10^{15}$ cm, 8.65$\times 10^{15}$ cm respectively.

In a study (Armijos-Abendaño et al., 2022) with XMM-Newton observations of NGC 7314 (and several other sources) using the hardness-ratio curves, the time intervals in which the clouds are eclipsing the central X-ray source has been investigated. They estimated that the eclipsing clouds with distances from the X-ray emitting region of 9.6$\times~10^{15}~{\rm cm}$ (or 3.6$\times~10^{4}~{\rm r_{g}}$ considering $M_{\rm BH}=10^{6}$ $M_{\odot}$) are moving at Keplerian velocities $\sim$1122 km/s. The distance of the clouds ($\sim 10^{16}$ cm) is similar to our estimated BLR radius. This indicates that the obscuring clouds are associated with BLR. To justify the line-width absorption, a high ionizing region, even closer to the BLR being the origin of the absorption, can not be overruled.

The soft excess in the spectra is modeled with a Bbody component. The temperature ($kT\sim 0.05$ keV) almost remained invariant for every combination of models. Even while fitting the different epoch XMM-Newton spectra, the temperature remains the same, except the normalization value was $\sim 0.08\pm 0.02$ for 2001 and 2016, and $\sim 0.06\pm 0.01$ for two 2013 observations. Although it is not certain about the origin of the soft excess (Pravdo et al., 1981; Arnaud et al., 1985; Turner & Pounds, 1989), however, this excess emission below 2 keV in X-ray is very common in narrow-line Seyfert 1 AGNs. Classically, this soft excess is modeled with a black body emission with a temperature of 0.1-0.2 keV (Walter & Fink, 1993; Czerny et al., 2003; Crummy et al., 2006). However, the temperature of the soft excess is too high to be directly emitted from the standard accretion disk (Shakura & Sunyaev, 1973). A narrow temperature range was obtained for a huge range of supermassive black holes (M$\sim 10^{6}-10^{8}~M_{\odot}$) when a sample of AGNs was modeled with a Compton scattered disk component (Gierliński & Done, 2004). The observed soft excess in the spectra could possibly be coming from the multiple scattering of the relatively high-energy photons. The soft excess could arise from the hot corona when seed photons suffer less scattering (Nandi et al., 2023). The hot plasma, responsible for the low variability of the high-energy photons, could be the origin of the soft excess.

The production of the narrow Fe K$\alpha$ line is often attributed to the reprocessing of central X-ray coronal emission by remote materials like the dusty torus (Krolik & Kallman, 1987; Nandra, 2006). Conversely, the broad Fe K$\alpha$ line is commonly thought to originate from the innermost section of the super-massive BH, most probably from the accretion disk or BLR (Nandra et al., 1997; Zoghbi et al., 2014; Kara et al., 2015). Its asymmetric profile is linked to relativistic beaming and gravitational redshift effects (Fabian, 1989; Fabian et al., 2000). Given the substantial distance and scale of the reprocessing material, it’s plausible that the narrow component exhibits considerably less variability than the broader component.

To estimate the parameters of these broad and narrow iron line features, we fit only the four individual spectra of XMM-Newton. The parameters of the broad and narrow Gaussian are given in the second part of Table 4. For constraining the line width of the narrow Gaussian line, we fixed the line width ($\sigma$) to 0.01 keV since it is not accurately resolved by the XMM-Newton data. The Fe K$\alpha$ line width of the broad component varies from $0.40\pm 0.07\rightarrow 0.33\pm 0.05\rightarrow 0.24\pm 0.07\rightarrow 0.37\pm 0.06$ keV. If we calculate the equivalent width of the broad Gaussian component, we see a similarity in 2001 ($EW\sim 0.20~{\rm keV}$) and 2016 ($EW\sim 0.19~{\rm keV}$) epochs, and 2013 epoch ($EW\sim 0.15~\&~0.14~{\rm keV}$). The narrow Fe K$\alpha$ line originates from the reflecting clouds located probably in the dusty torus. We estimate the approximate radius ($R_{{\rm Fe~K}\alpha}^{\rm broad/narrow}$) of the broad and narrow Fe K$\alpha$ line assuming the virial motion (Peterson et al., 2004; Andonie et al., 2022),

where $G$, $M_{\rm BH}$, and $\nu_{\textsc{fwhm}}$ are the Gravitational constant, the mass of the supermassive black hole, and the full width at half maximum calculated from the best-fitted parameters of Gaussian. It should be noted that we consider that the iron line emission is from the broad line region or from the outer dusty torus, not from the outflow. Otherwise, the virial motion for estimating the radius of the iron emission line would not be valid. We considered the mass of the supermassive black hole to be $5\times 10^{6}$ solar mass. The Gravitational constant value is $4.3\times 10^{-3}$ pc M${}_{\odot}^{-1}$ (km/s)². We obtain the Fe K$\alpha$ radius for the broad iron emission line to be $\sim~2.57\times 10^{14}$, $\sim~3.67\times 10^{14}$, $\sim~6.62\times 10^{14}$, and $\sim~3.05\times 10^{14}~{\rm cm}$ (or $8.33\times 10^{-5}~{\rm pc}$, $1.19\times 10^{-4}~{\rm pc}$, $2.15\times 10^{-4}~{\rm pc}$, and $9.88\times 10^{-5}~{\rm pc}$) respectively for the four observations. For the narrow component of the Fe K$\alpha$ line, the radius is $3.89\times 10^{19}~{\rm cm}$. It is to be noted that this is only an approximation as we could not be able to constrain the line width properly.

From the estimated radius of the iron emission line, the $R_{\rm dust}$ and the $R_{\rm BLR}$ (see, Section 4.3), we conclude that the emission comes from two different regions of the system. Broad iron line emission comes from very close to the central engine, possibly from the accretion disk, even closer than the BLR, and thus shows a variable nature. The narrow emission line possibly comes from the outer region of the torus and thus shows a constant nature.